How do you use the Curves modifier to make a smile or different shape?
First I would select your piece of jarn and press Alt + R to reset the rotation. I would do the alignment with the curve with translation (with G) and the axis-buttons on the settings of the Curve modifier alone. Then i would only manipulate the curve, not the jarn.
Apart from basic translation an rotation of the vertices of the curve, i would also Subdivide to create extra vertices for more control.
Lastly, and most importantly, it is useful to know you can rotate a curve vertex in Edit Mode around the length of the curve (in other words: adjust the tilt of the vertex) by pressing Ctrl + T.
twisted and untwisted:

Hope that helps.